rotation matrix generator

generateRotationMatrix.js

// This generates a matrix my multiplying matrix a and b and it generates
// another matrix that you use in your code with variables. This is a helpful
// way to auto generate matrices for stuff like rotation on X, Y, and Z.
//
// generateRotationMatrix([], [
//   1,   0,  0, 0,
//   0,  "cx", "sx", 0,
//   0, "-sx", "cx", 0,
//   0,   0,  0, 1,
// ], [
//   "cy", 0, "-sy", 0,
//   0, 1,   0, 0,
//   "sy", 0,  "cy", 0,
//   0, 0,   0, 1,
// ], [
//   "cz", "sz", 0, 0,
//   "-sz", "cz", 0, 0,
//   0, 0, 1, 0,
//   0, 0, 0, 1,
// ]);
//
// Will return:
// [
//   cz*cy, cz*sy*sx+sz*cx, -(cz*(sy*cx))+sz*sx, 0,
//   -(sz*cy), -(sz*sy*sx)+cz*cx, sz*(sy*cx)+cz*sx, 0,
//   sy, -(cy*sx), cy*cx, 0,
//   0, 0, 0, 1,
// ]
export function generateRotationMatrix(dest, ...mats) {
  return mats.reduce((a, b) => multiplyRotationMatrix(dest, a, b));
}

function multiplyRotationMatrix(dest, a, b) {
  const a00 = a[_00]; const b00 = b[_00];
  const a01 = a[_01]; const b01 = b[_01];
  const a02 = a[_02]; const b02 = b[_02];
  const a03 = a[_03]; const b03 = b[_03];
  const a10 = a[_10]; const b10 = b[_10];
  const a11 = a[_11]; const b11 = b[_11];
  const a12 = a[_12]; const b12 = b[_12];
  const a13 = a[_13]; const b13 = b[_13];
  const a20 = a[_20]; const b20 = b[_20];
  const a21 = a[_21]; const b21 = b[_21];
  const a22 = a[_22]; const b22 = b[_22];
  const a23 = a[_23]; const b23 = b[_23];
  const a30 = a[_30]; const b30 = b[_30];
  const a31 = a[_31]; const b31 = b[_31];
  const a32 = a[_32]; const b32 = b[_32];
  const a33 = a[_33]; const b33 = b[_33];

  const multiplyString = (a, b) => {
    if (!a || !b) {
      return 0;
    }
    if (a === 1) {
      return b;
    }
    if (b === 1) {
      return a;
    }
    if (a[0] === "-" && b[0] === "-") {
      return a.substr(1) + "*" + b.substr(1);
    }
    if (a[0] === "-") {
      return "-(" + a.substr(1) + "*" + b + ")";
    }
    if (b[0] === "-") {
      return "-(" + a + "*" + b.substr(1) + ")";
    }
    return a + "*" + b;
  }

  const fixResult = (s) => {
    if (!s) {
      return 0;
    }
    if (s === "1") {
      return 1;
    }
    return s;
  }

  // First row = first row of B times all columns of A
  dest[0] = [multiplyString(b00, a00), multiplyString(b01, a10), multiplyString(b02, a20), multiplyString(b03, a30)].filter(Boolean).join("+");
  dest[1] = [multiplyString(b00, a01), multiplyString(b01, a11), multiplyString(b02, a21), multiplyString(b03, a31)].filter(Boolean).join("+");
  dest[2] = [multiplyString(b00, a02), multiplyString(b01, a12), multiplyString(b02, a22), multiplyString(b03, a32)].filter(Boolean).join("+");
  dest[3] = [multiplyString(b00, a03), multiplyString(b01, a13), multiplyString(b02, a23), multiplyString(b03, a33)].filter(Boolean).join("+");

  // Second row = second row of B times all columns of A
  dest[4] = [multiplyString(b10, a00), multiplyString(b11, a10), multiplyString(b12, a20), multiplyString(b13, a30)].filter(Boolean).join("+");
  dest[5] = [multiplyString(b10, a01), multiplyString(b11, a11), multiplyString(b12, a21), multiplyString(b13, a31)].filter(Boolean).join("+");
  dest[6] = [multiplyString(b10, a02), multiplyString(b11, a12), multiplyString(b12, a22), multiplyString(b13, a32)].filter(Boolean).join("+");
  dest[7] = [multiplyString(b10, a03), multiplyString(b11, a13), multiplyString(b12, a23), multiplyString(b13, a33)].filter(Boolean).join("+");


  // Thrid row = third row of B times all columns of A
  dest[8] = [multiplyString(b20, a00), multiplyString(b21, a10), multiplyString(b22, a20), multiplyString(b23, a30)].filter(Boolean).join("+");
  dest[9] = [multiplyString(b20, a01), multiplyString(b21, a11), multiplyString(b22, a21), multiplyString(b23, a31)].filter(Boolean).join("+");
  dest[10] = [multiplyString(b20, a02), multiplyString(b21, a12), multiplyString(b22, a22), multiplyString(b23, a32)].filter(Boolean).join("+");
  dest[11] = [multiplyString(b20, a03), multiplyString(b21, a13), multiplyString(b22, a23), multiplyString(b23, a33)].filter(Boolean).join("+");

  // Fourth row = fourth row of B times all columns of A
  dest[12] = [multiplyString(b30, a00), multiplyString(b31, a10), multiplyString(b32, a20), multiplyString(b33, a30)].filter(Boolean).join("+");
  dest[13] = [multiplyString(b30, a01), multiplyString(b31, a11), multiplyString(b32, a21), multiplyString(b33, a31)].filter(Boolean).join("+");
  dest[14] = [multiplyString(b30, a02), multiplyString(b31, a12), multiplyString(b32, a22), multiplyString(b33, a32)].filter(Boolean).join("+");
  dest[15] = [multiplyString(b30, a03), multiplyString(b31, a13), multiplyString(b32, a23), multiplyString(b33, a33)].filter(Boolean).join("+");

  return dest.map(fixResult);
};